BUDGET CONSTRAINT

Budget Constraint Economists assume that consumers choose the best bundle that they can afford (Rationality assumption) Suppose there are two goods . Budget Constraint: Budget Set shows all the affordable bundles

Budget Set and Line x2 Budget line is m /p2 p1x1 + p2x2 = m. x1 m /p1 Not affordable Just affordable Affordable m /p1 x1

Budget Set and Line x2 Budget line is m /p2 p1x1 + p2x2 = m. the collection of all affordable bundles. Budget Set m /p1 x1

Budget Set and Line x2 p1x1 + p2x2 = m is m /p2 x2 = -(p1/p2)x1 + m/p2 so slope is -p1/p2. m /p2 Budget Set m /p1 x1

Slope of Budget Line For x1 on the horizontal axis, the budget line’s slope is -p1/p2. What does it mean? With the given income, to increase the consumption of x1 by 1, p1/p2 units of x2 should be given up. ( i.e. opportunity cost of good 1 in term of good 2)

Slope of Budget Line x2 Opportunity cost of an extra unit of good 1 is p1/p2 units foregone of good 2. -p1/p2 +1 x1

Budget Sets & Lines; Income and Price Changes The budget line and budget set depend upon prices and income. What happens as prices or income change?

How do the budget set and budget line change as income m increases? x2 New affordable consumption choices Original and new budget lines are parallel (same slope). Original budget set x1

How do the budget set and budget line change as income m decreases? x2 Consumption bundles that are no longer affordable. Old and new lines are parallel. New, smaller budget set x1

Budget Lines - Income Changes Increases in income m shift the line outward in a parallel manner, thereby enlarging the budget set and improving choice. Decreases in income m shift the line inward in a parallel manner, thereby shrinking the budget set and reducing choice.

Budget Lines - Price Changes What happens if just one price decreases? Suppose p1 decreases.

New affordable choices How do the budget set and budget line change as p1 decreases from p1’ to p1”? x2 m/p2 New affordable choices Budget line pivots; slope flattens from -p1’/p2 to -p1”/p2 -p1’/p2 Original budget set -p1”/p2 m/p1’ m/p1” x1

Budget Line - Price Changes Reducing the price of one commodity pivots the constraint outward. Similarly, increasing one price pivots the constraint inwards

Examples of Budget Lines Uniform Ad Valorem Sales Taxes: Ad Valorem tax is a tax on value (i.e. the price) of a good. An uniform ad valorem sales tax levied at a rate of 5% increases all prices by 5%, from p to (1+0×05)p = 1×05p. An uniform ad valorem sales tax levied at a rate of t increases all prices by tp from p to (1+t)p.

Uniform Ad Valorem Sales Taxes A uniform sales tax levied at rate t changes the line from p1x1 + p2x2 = m to (1+t)p1x1 + (1+t)p2x2 = m i.e. p1x1 + p2x2 = m/(1+t).

Uniform Ad Valorem Sales Taxes p1x1 + p2x2 = m p1x1 + p2x2 = m/(1+t) x1

Examples of Budget Lines Coupons: (ex: Food Stamps) Food stamps are coupons that can be legally exchanged only for food.

The Food Stamp Program Suppose m = $100, pF = $1 and the price of “other goods” is pG = $1. The budget line is then F + G =100. How does 40 food stamps alter the budget line? (assuming that with each food stamp, consumer can get 1 unit of food)

The Food Stamp Program G F + G = 100: before stamps. 100 F 100

The Food Stamp Program G F + G = 100: before stamps. 100 Budget set after 40 food stamps issued. The budget set is enlarged. F 40 100 140

Examples of Budget Lines Quantity Discount: Suppose p2 is constant at $1 but that p1=$2 for 0 £ x1 £ 20 and p1=$1 for x1>20 (i.e. each additional unit of good 1 purchased after 20 units). Then the line’s slope is - 2, for 0 £ x1 £ 20 -p1/p2 = - 1, for x1 > 20 {

Quantity Discount x2 m = $100 Slope = - 2 / 1 = - 2 (p1=2, p2=1) 20 50 80

Quantity Discount x2 m = $100 Slope = - 2 / 1 = - 2 (p1=2, p2=1) 20 50 80

Quantity Discount x2 m = $100 100 Budget Line Budget Set x1 20 50 80

Examples of Budget Lines Other Examples: (Will be discussed in class) Per unit tax Per unit tax after certain amount Rationing